Currently available transmissions for heavy working machinery typically have a multi-speed “input” section driving into either a two-speed high/low ratio “splitter” section or a three speed high/medium/low ratio “splitter” section. By successively engaging torque-transmitting mechanisms in the input section (“input torque-transmitting mechanisms”) with the splitter section torque-transmitting mechanisms a shift sequence is achieved. For instance, if the input section includes torque-transmitting mechanisms A, B, C and the splitter section includes torque-transmitting mechanisms low (L), medium (M) and high (H) then the shift sequence would be AL-BL-CL-AM-BM-CM-AH-BH-CH. This shift sequence has single transition shifting except for two undesirable center shifts, i.e., CL to AM and CM to AH. These are double transition shifts which compromise shift quality, shift time and durability of the internal gears.